Botswana on Tuesday said it would deport a Holocaust-denying, anti-gay American pastor, declaring him a "prohibited immigrant".

Steven Anderson, who in 2009 infamously prayed for US President Barack Obama's death, was arrested by immigration officials shortly after being interviewed on a popular radio station.

The Christian preacher arrived in Botswana last Thursday for a "soul-winning" event, just days after he was banned from visiting South Africa over his characterisation of gays as "sodomites" and "paedophiles."

"This is to confirm the Pastor Steven Anderson, a citizen of the United States of America, has been declared a Prohibited Immigrant and as such is being deported from Botswana," the government said in a brief statement.

It did not disclose the reason behind the decision.

Anderson has frequently courted controversy through his Arizona-based Faithful Word Baptist Church, which preaches a literal reading of the Bible.

A Holocaust denier, he prayed for the death of US President Barack Obama in 2009 over his pro-choice stance on abortion, and called the victims of the November 2015 attack on the Bataclan nightclub in Paris "devil worshippers".

After the deadly shooting at a gay nightclub in Orlando earlier this year, he said "there's 50 less paedophiles in this world".

Speaking to Gabz FM on Tuesday morning, Anderson criticised "drunkenness and alcoholism" in Botswana, and repeated his views on homosexuality, calling a gay guest on the show "disgusting".

"He should be killed," the pastor said.

Immigration officials arrived at the studio during the interview and escorted Anderson to the immigration department to be deported.